D.A.V. PUBLIC SCHOOL, NEW PANVEL

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D.A.V. PUBLIC SCHOOL, NEW PANVEL
Plot No. 267, 268, Sector-10, New Panvel,
Navi Mumbai-410206 (Maharashtra).
Phone 022-27468211, 27451793, 27482276
E-mail – [email protected], www.davnewpanvel.com
PRACTICE PAPER FOR
II PREPARATORY EXAMINATION 2015-2016
STD:- IX
Sub: - Mathematics
Time: - 3 Hours
Date: Marks: - 90
……………………………………………………………….………………………………………....
General Instructions:1. All questions are compulsory.
2. The question paper consists of 31 questions divided into 5 sections–A, B,C,D and E.
i) Section A comprises 4 questions of 1 mark each.
ii) Section B comprises 5 questions of 2 marks each.
iii) Section C comprises 10 questions of 3 marks each.
iv) Section D comprises 9 questions of 4 marks each.
v) Section E comprises 3 questions of 10 marks. This section is based on OTBA.
3. In questions on construction, the drawing should be neat and exactly as per the
given measurements. Use ruler and compass only.
………………………………………………………………………………………………………
SECTION – A
1. For what value of p the point ( p, 2 ) lies on the line 3x + y = 11?
2. Diagonals of quadrilateral ABCD bisect each other. If ∠ A = 350, determine ∠ B.
3. The curved surface area of a right circular cylinder of height 14cm is 88cm2. Find the
radius of the base of the cylinder.
4. What is the probability of a sure event?
SECTION – B
5. If the point (3,4) lies on the graph of 3x = ay + 7,find the value of a.
6. How many solution(s) of the equation 3x + 2 = 2x – 3 are there on the number line
and Cartesian plane?
7. In the figure A, B, C and D are four points on a circle.AC and BD intersect at point E
such that ∠ BEC = 1300 and ∠ ECD = 200.Find ∠ BAC.
8. A joker’s cap is in the form of a right circular cone of base radius 7cm and height
24cm2. Find the area of the sheet required to make one cap.
9. Three cubes each of side 6cm are joined end to end. Find the total surface area of
the resulting figure obtained.
SECTION – C
10. A family spends Rs 500 monthly as a fixed amount on milk and extra milk costs
Rs 20 per kg. Taking quantity of extra milk as x and total expenditure on milk as y.
Write a linear equation and fill the table.
x
y
0
2
1000
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11. In a parallelogram ABCD, E and F are the mid points of sides AB and CD
respectively. Show that the line segment AF and EC trisect the diagonal BD. ∆ ABC, E is the midpoint of median AD. Show that
1
ar( ∆ BED) = ar ( ∆ ABC.)
4
13. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices
of the quadrilateral, prove that it is a rectangle.
12. In
a
14. A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and
David are sitting at equal distance on its boundary each having a toy telephone in
his hands to talk each other. Find the length of the string of each phone.
15. Construct a triangle with the base of 5cm, the sum of other two sides are 7cm and
one base angle of 600.
16. The diameter of a metallic ball is 4.2cm.What is the mass of the ball, if the density
of the metal is 8.9gm per cm3?
17. Find the cost of digging a cuboidal pit 8m long, 6m broad and 3m deep at the rate
of Rs 30 per m3.
18. The hemispherical dome of a building needs to be painted. If the circumference of
the base of the dome is 17.6m, find the cost of painting it, given the cost of painting
is Rs 5 per 100cm2.
19. A tyre manufacturing company kept a record of the distance covered before a tyre
needed to be replaced. The table shows the result of 1000 cases.
Distance
in km
Frequency
Less than
4000
20
4000 - 9000
9000 - 14000
210
325
More than
14000
445
If someone buys a tyre of this company, what is the probability that:
i) It will need to be replaced before it has covered 4000km?
ii) It will last more than 9000km?
iii) It will need to be replaced after it has covered somewhere between
4000 and 14000km?
SECTION D
20. The linear equation that converts Fahrenheit(F) in Celsius (C) given by the relation
5 F − 160
C=
9
i) If the temperature is 860F, what is the temperature in Celsius?
ii) If the temperature is 350 C, what is the temperature in F?
iii) What is the numerical value of the temperature which is same in both the
scales?
iv) If the temperature is 00 Celsius, what is the temperature in Fahrenheit and if
the temperature is 00 Fahrenheit, what is the temperature in Celsius?
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21.
The auto rickshaw fare in a city is charged as Rs.10 for the first km and
Rs. 4 per km for subsequent distance covered. Write the linear equation to
express the above statement. Draw the graph of linear equation.
22.
D,E,F are respectively the midpoints of the sides BC,CA and AB of ∆ ABC .
Show that i) BDEF is a parallelogram ii) ar( ∆ DEF) =
iii) ar( ║gmBDEF) =
1
4
ar( ∆ ABC)
1
ar( ∆ ABC).
4
23.
Show that the diagonals of a square are equal and bisect each other at
right angles.
24.
The angle subtended by an arc at the centre is double the angle subtended
by it at any point on the remaining part of the circle.
25.
A villager has a plot of land of the shape of a quadrilateral .The Gram Panchayat
of the village decided to take over some portion of his plot from one of the corners
to construct a health centre. Villager agrees to the above proposal with the
condition that he should be given equal amount of land in lieu of his land adjoining
his plot so as to form a triangular plot. Explain how the proposal will be
implemented?
1
50 circular plates, each of radius 7cm and thickness cm are placed one above
2
other to form a right circular cylinder. Find the total surface area and volume of
cylinder so formed.
26.
27.
In a school 120 students took part in Vanmahotsva and helped each other in
planting the plants to make the campus of school beautiful.
Name of plants
Number of plants
Rose
46
Marigold
18
Chameli
22
Jasmine
34
Find the probability of planting
i) Rose
ii) Jasmine
iii) Marigold and Chameli
iv) Which value has been shown by the students?
28.
Construct a ∆ ABC in which ∠ B=600, ∠ C=450 and AB+BC+CA=11cm.
SECTION E
TITLE : AATITHI DEVO BHAVA
29.
Find the mean of number of FTAs from different regions of the world in 2011.
30.
Prepare a frequency polygon on the percentage distribution of FTAs in
India according to age groups during 1996-2012.
31.
i) On the basis of bar graph given on arrival of FTAs in India which travel is most
preferred and why?
ii) What is the probability of FTAs comprises of males and females during the
year 2012.
iii) Find the median of the data of FTAs from different regions of the world in 2012.
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